Attractive Force of Spherical Capacitors

Electricity and Magnetism Level 3

If a capacitor is composed of two isolated conductors, after charging the oppositely charged plates will experience a Coulombic attraction. Given a spherical capacitor of inner radius $a$ and outer radius $b$ , find the attractive force exerted on the outer conductor assuming that each conductor holds charge $\pm Q$ .

Assume the conductors are mechanically held fixed, so the force is constant in time, and let negative forces correspond to attraction and vice versa.

-\frac{Q^2}{4\pi \epsilon_0 b^2}

-\frac{Q^2}{4\pi \epsilon_0 ab}

-\frac{Q^2}{8\pi \epsilon_0 b^2}

-\frac{Q^2}{8\pi \epsilon_0 ab}